Projection lens with four glass elements having spherical surfaces

ABSTRACT

A projection lens can include four lens elements, each lens element being formed from glass and including spherical or planar incident and exiting surfaces. Compared to a projection lens that uses three lens elements, the four-element projection lens has relaxed manufactured and alignment tolerances. Unlike a projection lens that uses one or more plastic elements or uses aspherical surfaces, the all-glass projection lens can be manufactured using relatively fast and inexpensive grinding and polishing techniques. One or two of the glass lens elements can optionally be formed symmetrically, so as to be reversible. One glass element can optionally be piano-convex. A right-angle prism can direct light from a video display into the four glass elements. An achromatic prism can angularly divert the optical axis by about eight degrees and can direct light out of the four glass elements into a near-eye waveguide.

PRIORITY CLAIM

This application claims the benefit of priority to U.S. ProvisionalPatent Application Ser. No. 62/758.277, filed on Nov. 9, 2018, thebenefit of priority which is claimed hereby, and is incorporated byreference herein in its entirety.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to optical systems suitable foruse in near-eye displays.

BACKGROUND OF THE DISCLOSURE

A near-eye display can produce a video image, and direct the video imagetoward a human eye. In many cases, components in an optical system in anear-eye display can be difficult to manufacture and align, due torelatively tight tolerances, and/or expensive, due to relativelyexpensive manufacturing techniques.

As a result, there exists a need for a near-eye display optical systemthat has relatively loose tolerances and is manufacturable usingrelatively inexpensive manufacturing techniques.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic view of an optical system suitable for use in anear-eye display, in accordance with some embodiments.

FIG. 2 shows a side view of an example of an optical system suitable foruse in a near-eye display, in accordance with some embodiments.

FIG. 3 shows a top view of the optical system of FIG. 2, where theright-angle prism is unfolded for clarity.

Corresponding reference characters indicate corresponding partsthroughout the several views. Elements in the drawings are notnecessarily drawn to scale. The configurations shown in the drawings aremerely examples, and should not be construed as limiting the scope ofthe inventive subject matter in any manner.

DETAILED DESCRIPTION

A near-eye display can include a projection lens. The projection lenscan include four lens elements, each lens element being formed fromglass and including spherical or planar incident and exiting surfaces.Compared to a projection lens that uses three lens elements, thefour-element projection lens can have relaxed manufactured and alignmenttolerances. Unlike a projection lens that uses one or more plasticelements or uses aspherical surfaces, the all-glass projection lens canbe manufactured using relatively fast and inexpensive grinding andpolishing techniques. One or two of the glass lens elements canoptionally be formed symmetrically, so as to be reversible. One glasselement can optionally be plano-convex. A right-angle prism can directlight from a video display into the four glass elements. An achromaticprism can angularly divert the optical axis by about eight degrees andcan direct light out of the four glass elements into a near-eyewaveguide.

In the following discussion, the Abbe number (also known as V-number) ofa material is defined as defined as the dimensionless quantity(n_(d)−1)/(n_(F)−n_(C)), where nd is a refractive index of the materialat a wavelength of 587.6 nm (helium d-line), n_(F) is a refractive indexof the material at a wavelength of 486.1 nm (hydrogen F-line), and n_(C)is a refractive index of the material at a wavelength of 656.3 nm(hydrogen C-line). In general, the higher the Abbe number of a material,the lower the dispersion of the material.

In the discussion that follows, various optical elements are referred toas first lens element, second lens element, and so forth. It will beunderstood that the numbering scheme is provided merely for convenience,and to specify an order in which the numbered elements appear. In someexamples, one or more additional optical elements can optionally appearbetween the numbered elements. For example, a planar spectral filter canappear before a first lens element, between a first lens element and asecond lens element, between a second lens element and a third lenselement, and so forth.

FIG. 1 shows a schematic view of an optical system 100 suitable for usein a near-eye display, in accordance with some embodiments. Theconfiguration of FIG. 1 is but one configuration; other suitableconfigurations can also be used.

The optical system 100 can include a controller 102. The controller 102can include circuitry that can convert data representing a video imageinto an electrical signal. The circuitry can include a processor 104.The circuitry can include memory 106. The memory 106 can includeinstructions that, when executed by the processor 104, cause theprocessor 104 to execute instructions. The instructions can includeprocessing the electrical signal, storing and accessing stored videocontent, and the like. The controller 102 can direct a video signal tothe display 108 to be displayed on the display 108. The controller 102can include a processor 104 on or in the display 108, or can be coupledto a processor 104 away from the display 108 via a wired and/or wirelessconnection. The controller 102 can optionally receive data correspondingto the video signal from an external source, such as a video gameconsole, a laptop or computer connected by a wired or wirelessconnection, a streaming video source, or others. In some examples, thedisplay 108 can be a liquid crystal on silicon (LCOS) or a digital lightprocessing (DLP) display, in which is illuminated externally. Thedisplay 108 can display a video image corresponding to the electricalsignal. A projection lens 110 (discussed in detail below) can projectthe video image from the display 108 into a near-eye waveguide 112. Thenear-eye waveguide 112 can guide the projected video image to a locationproximate a human eye 114. Light from the waveguide 112 can enter thehuman eye 114. The light can form a reproduced video image on the retinaof the human eye 114, which corresponds to the video image displayed onthe display 108 and the corresponding electrical signal.

The elements in FIG. 1 (except the human eye 114) can be packaged as anear-eye display, and can optionally be worn as eyewear, such asspectacles, or as a head-mounted display.

The projection lens 110 is discussed in detail below.

FIG. 2 shows a side view of an example of an optical system 110 suitablefor use in a near-eye display, in accordance with some embodiments. FIG.3 shows a top view of the optical system 110 of FIG. 2, where theright-angle prism is unfolded for clarity.

The display 108 can display video, which can include a sequence ofimages that refreshes at a video rate, such as 30 Hz, 60 Hz, 90 Hz, 120Hz, or another suitable video rate. In some examples, the display 108can include an array of pixels, each of which can be independentlycontrolled.

In some examples, the display 108 can include sequential colorillumination. For example, a red light emitting diode can be activated,and the pixels corresponding to the red portions of the image can besimultaneously activated to the “on” state. Then, a green light emittingdiode can be activated, with corresponding pixels, followed by a bluelight emitting diode with corresponding pixels. The red, green, and blueillumination and pixel activation can be cycled as needed to form avideo image that includes contributions from the red, green, and bluepixels. In other examples, each pixel can include a red light-producingelement, a green light-producing element, and a blue light-producingelement, each of which are independently controllable to produce adesired intensity (e.g., brightness) and color for each pixel. In someexamples, other suitable colors can be used. In some examples, eachlight-producing element can be a light-emitting diode. In some examples,each light-producing element can be a laser diode. In some examples,each light-producing element can include a white-light source followedby a suitable spectral filter. In some examples, the display 108 can berectangular, square, oval, or another suitable shape. In some examples,the display 108 be relatively small, such as approximately 3 mm along anedge. Other sizes can also be used.

The display 108 can optionally be packaged behind a cover glass 216,which is typically a relatively thin glass element. The cover glass 216is intended to protect the display 108 from dust and contamination, andgenerally does not play an optical role in the system.

A near-eye waveguide 112 can operably guide light toward a human eye 114(FIG. 1). In some examples, the near-eye waveguide 112 can be shaped asan elongated element having a rectangular or square cross-section thatremains constant along a longitudinal length of the near-eye waveguide112. Other shapes and configurations can also be used for the near-eyewaveguide 112. The projection lens 110 described below can receive lightfrom the display 108 and direct the light into the near-eye waveguide112. When the near-eye waveguide 112 is positioned suitably close to ahuman eye 114, the near-eye waveguide 112 can direct the light into thehuman eye 114.

A projection lens 110 having a positive total refractive power candirect light from the displayed video in a light ray bundle from thedisplay 108 into the near-eye waveguide 112. The projection lens 110 canhave an optical axis (OA) that corresponds to a center of the light raybundle.

The projection lens 110 can include a right-angle prism 218 positionedalong the optical axis (OA) adjacent the display 108. The right-angleprism 218 can angularly divert the optical axis (OA) by ninety degrees.In some examples, the angles can deviate away from the 45 degree/45degree/90 degree geometry of a true right-angle prism 218, so that theangular diversion can deviate away from ninety degrees. Other suitableangular deviations can include ranges between 89 and 91 degrees, between88 and 92 degrees, between 85 and 95 degrees, and others. Theright-angle prism 218 can be formed from a crown glass having arefractive index greater than or equal to 1.728 at a wavelength of 587.6nm and an Abbe number (which measures a glass's dispersion, or itsvariation in refractive index as a function of wavelength) greater than50. Suitable high-index crown glasses can include H-LAK52, having arefractive index of 1.729 at a wavelength of 587.6 nm and an Abbe numberof 54.7. Other suitable high-index crown glasses can also be used.

The projection lens 110 can include a first lens element 220 positionedalong the optical axis (OA) and formed from a first glass having arefractive index between 1.72 and 1.85 at a wavelength of 587.6 nm andan Abbe number between 40 and 55. Suitable glasses can include H-LAF50B(having a refractive index of 1.773 at a wavelength of 587.6 nm and anAbbe number of 49.6), KLASKN1, HLAK53B, and others. The first lenselement 220 can have a convex spherical first incident surface 222facing the right-angle prism 218 and a convex spherical first exitingsurface 224 facing away from the display 108. In some examples, thefirst incident surface 222 and the first exiting surface 224 can have asame radius of curvature, which can simplify a manufacturing process forthe first lens element 220. The first incident surface 222, the firstexiting surface 224, and the first glass can define a refractive powerof the first lens element 220 to be positive and between 88% and 128% ofthe total refractive power, positive and between 112% and 128% of thetotal refractive power, or in another suitable range.

The projection lens 110 can include a second lens element 226 positionedalong the optical axis (OA) and formed from second glass having arefractive index between 1.72 and 1.85 at a wavelength of 587.6 nm andan Abbe number between 38 and 55. Suitable glasses can include H-ZLAF50E(having a refractive index of 1.804 at a wavelength of 587.6 nm and anAbbe number of 46.6). D-ZLAF85L, SLAH59, TAF3D, and others. The secondlens element 226 can have a convex spherical second incident surface 228facing the first lens element 220 and a concave spherical second exitingsurface 230 facing away from the first lens element 220. The secondincident surface 228, the second exiting surface 230, and the secondglass can define a refractive power of the second lens element 226 to bepositive and between 35% and 68% of the total refractive power, positiveand between 35% and 54% of the total refractive power, or in anothersuitable range. In some examples, the refractive power of the secondlens element 226, divided by the refractive power of the first lenselement 220, can be between 0.28 and 0.71, between 0.28 and 0.46, or inanother suitable range.

The projection lens 110 can include a third lens element 232 positionedalong the optical axis (OA) and formed from a third glass having arefractive index greater than 1.8 at a wavelength of 587.6 nm and anAbbe number between 20 and 24. Suitable glasses can include H-ZF62(having a refractive index of 1.923 at a wavelength of 587.6 nm and anAbbe number of 20.9), KPSFN 1M, and others. The third lens element 232can have a concave spherical third incident surface 234 facing thesecond lens element 226 and a concave spherical third exiting surface236 facing away from the second lens element 226. In some examples, thethird incident surface 234 and the third exiting surface 236 can have asame radius of curvature, which can simplify a manufacturing process forthe third lens element 232. The third incident surface 234, the thirdexiting surface 236, and the third glass can define a refractive powerof the third lens element 232 to be negative and between 165% and 216%of the total refractive power, negative and between 183% and 216% of thetotal refractive power, or in another suitable range.

The projection lens 110 can include a fourth lens element 238 positionedalong the optical axis (OA) and formed from a fourth glass having arefractive index greater than 1.85 at a wavelength of 587.6 nm and anAbbe number between 28 and 35. Suitable glasses can include H-ZLAF75B(having a refractive index of 1.904 at a wavelength of 587.6 nm and anAbbe number of 31.4), TAFD55, H-ZLAF76, and others. The fourth lenselement 238 can have a convex spherical or planar fourth incidentsurface 240 facing the third lens element 232 and a convex sphericalfourth exiting surface facing away from the third lens element 232toward the near-eye waveguide 112. The fourth incident surface 240, thefourth exiting surface 242, and the fourth glass can define a refractivepower of the fourth lens element 238 to be positive and between 87% and125% of the total refractive power, positive and between 91% and 125% ofthe total refractive power, or in another suitable range. In someexamples, the refractive power of the fourth lens element 238, dividedby the refractive power of the third lens element 232, can be between−0.64 and −0.49, between −0.60 and −0.49, or in another suitable range.

In some examples, the first incident surface 222, the first exitingsurface 224, the second incident surface 228, the second exiting surface230, the third incident surface 234, the third exiting surface 236, thefourth incident surface 240 (for cases in which the fourth incidentsurface 240 is spherical. e.g., non-planar), and the fourth exitingsurface 242 have centers that are collinear along the optical axis (OA).Specifically, each of these surfaces can have a vertex that intersectsthe optical axis (OA).

In general, the glass materials for the first lens element 220, thesecond lens element 226, the third lens element 232, the fourth lenselement 238, and the right-angle prism 218 can be selected to reduce orminimize chromatic aberration, at a system level (e.g., one or moreelements having a positive chromatic aberration, one or more elementshave a negative chromatic aberration, and the net summed chromaticaberration being at or close to zero), for light passing through theseelements.

The projection lens 110 can include an achromatic prism 244 positionedalong the optical axis (OA) between the fourth lens element 238 and thenear-eye waveguide 112. The achromatic prism 244 can angularly divertthe optical axis (OA) by an angle between seven degrees and ninedegrees, such as eight degrees. Other suitable angular diversions canalso be used, such as a range between six degrees and ten degrees,between three degrees and thirteen degrees, and others.

In some examples, the achromatic prism 244 can be formed from a firstprism element 246, facing the fourth lens element 238, in contact with asecond prism element 248, facing the near-eye waveguide 112. In someexamples, the first prism element 246 can be formed from a flint glasshaving a refractive index between 1.85 and 2.01 at a wavelength of 587.6nm and an Abbe number between 18.0 and 23.8. Suitable glasses caninclude H-ZF52 (having a refractive index of 1.847 at a wavelength of587.6 nm and an Abbe number of 23.8), P-SF68. H-ZF88, H-ZF72A, H-ZF62,and others. In some examples, the second prism element 248 can be formedfrom a crown glass having a refractive index of 1.73 at a wavelength of587.6 nm and an Abbe number of 54.7. Suitable glasses can includeH-LAK52 (having a refractive index of 1.729 at a wavelength of 587.6 nmand an Abbe number of 54.7), and others. In some examples, the glassesfor the first prism element 246 and the second prism element 248 can beselected to reduce or minimize the chromatic aberration of theachromatic prism 244 (e.g., so that the net chromatic aberration of theachromatic prism 244, alone, is zero or a relatively small value).

In some examples, the projection lens 110 can operate over a wavelengthrange of 460 nm to 620 nm, inclusive. Other suitable wavelength rangescan also be used, including 400 nm to 700 nm (typically considered to bea full wavelength range of typical human vision), and others.

The f/# of a lens can quantify the cone of light captured by the lensfor a single object point. Specifically, for a single pixel on thedisplay 108, the f/# can characterize the size of the angular range,from the pixel, that is captured by the projection lens 110. In someexamples, f/# can be related to an amount of light captured by the lens.For example, a relatively low f/# means that more light is captured bythe lens, and an image formed by the lens is relatively bright.Similarly, a higher f/# means that less light is captured by the lens,and an image formed by the lens is relatively dim. In some examples, theprojection lens 110 can operate at an f/# of 2.08, which corresponds toa numerical aperture of 0.24 at the display 108, or a half-angle ofabout 14 degrees at the display 108. Other suitable values can also beused.

The field of view of a lens can quantify how much area of an object iscaptured by the lens. Specifically, the field of view should include all(or nearly all) of the display 108, so that the lens captures light frompixels at the edge of the display 108. In some examples, the projectionlens 110 can have a field of view of 25 degrees, diagonal. Othersuitable values can also be used.

The effective focal length is a distance between a rear principal pointof a lens and a rear focal point of the lens. Both the rear principalpoint and the rear focal point are locations in the lens. Both aremathematical constructs, rather than tangible physical elements of alens. In some examples, the projection lens 110 can have an effectivefocal length of 8.32 mm. Other suitable values can also be used.

The distortion of a lens is one measure of how accurately pixellocations are mapped between an object and a corresponding image. In thecomplete absence of distortion, a square object is mapped to a squareimage, with the square image having perfectly straight sides. Inpractice, it is generally difficult to completely eliminate distortion,so a lens designer often attempts to reduce distortion as much as ispractical, and expresses a residual distortion as a percentage of animage height. In some examples, the projection lens 110 can have adistortion of 0.75% at an image height of 1.86 mm. Other suitable valuescan also be used.

The telecentricity of a lens can affect a brightness of an image formedby the lens. For a projection lens 110 with a display that is externallyilluminated (e.g., a multi-pixel attenuator that attenuates light from alight source), telecentricity is desirable, so that pixels at the edgeof the image are as bright as pixels in the center of the image. In someexamples, the projection lens 110 can have a telecentricity of less than0.5 degree (chief ray angle) at the edge of the image field (e.g.,corresponding to a diagonal corner of the display 108). A quantityrelated to telecentricity is relative illumination. In some examples,the projection lens 110 can have a relative illumination (relative to acenter of the image) of greater than or equal to 80% at an image heightof 1.86 mm. Other suitable values can also be used.

In general thermal performance of a lens can be important. For example,it can be desirable to manage thermal expansion of the lens materials,and thermal variations in refractive index, so that the lens performancesuitably well over a range of temperatures. In some examples, theprojection lens 110 can have an athermal operation over a temperaturerange of seventy degrees. Other suitable values can also be used.

In some examples, the exit pupil of the projection lens 110 can beexternal to the lens elements. For example, the exit pupil can belocated at or near an area on the near-eye waveguide 112 at which lightenters the near-eye waveguide 112. In some examples, the distancebetween an external aperture stop to a vertex of the exiting surface ofthe fourth lens element 238 can be between 3.4 mm to 3.6 mm. Othersuitable values can also be used.

In some examples, a total lens length can represent a distance in airbetween a vertex of the incident surface of the first lens element 220and a vertex of the exiting surface of the fourth lens element 238. Insome examples, the total lens length can be 6.59 mm. Other suitablevalues can also be used.

In some examples, an object distance can represent a distance in airbetween the display 108 and a vertex of the first incident surface 222of the first lens element 220. In some examples, the object distance canbe 6.1 mm. Other suitable values can also be used.

While this invention has been described as having example designs, thepresent invention can be further modified within the spirit and scope ofthis disclosure. This application is therefore intended to cover anyvariations, uses, or adaptations of the invention using its generalprinciples. Further, this application is intended to cover suchdepartures from the present disclosure as come within known or customarypractice in the art to which this invention pertains and which fallwithin the limits of the appended claims.

To further illustrate the device disclosed herein, a non-limiting listof examples is provided below. Each of the following non-limitingexamples can stand on its own, or can be combined in any permutation orcombination with any one or more of the other examples.

In Example 1, an optical system can include: a projection lens having apositive total refractive power and configured to direct light in alight ray bundle from a display into a near-eye waveguide, theprojection lens having an optical axis that corresponds to a center ofthe light ray bundle, the projection lens comprising: a first lenselement positioned along the optical axis, the first lens element havinga convex spherical first incident surface facing the display and aconvex spherical first exiting surface facing away from the display; asecond lens element positioned along the optical axis, the second lenselement having a convex spherical second incident surface facing thefirst lens element and a concave spherical second exiting surface facingaway from the first lens element; a third lens element positioned alongthe optical axis, the third lens element having a concave sphericalthird incident surface facing the second lens element and a concavespherical third exiting surface facing away from the second lenselement; and a fourth lens element positioned along the optical axis,the fourth lens element having a convex spherical or planar fourthincident surface facing the third lens element and a convex sphericalfourth exiting surface facing away from the third lens element.

In Example 2, the optical system of Example 1 can optionally be furtherconfigured such that the first lens element is formed from a first glasshaving a refractive index between 1.72 and 1.85 at a wavelength of 587.6nm and an Abbe number between 40 and 55; the second lens element isformed from second glass having a refractive index between 1.72 and 1.85at a wavelength of 587.6 nm and an Abbe number between 38 and 55; thethird lens element is formed from a third glass having a refractiveindex greater than 1.8 at a wavelength of 587.6 nm and an Abbe numberbetween 20 and 24; and the fourth lens element is formed from a fourthglass having a refractive index greater than 1.85 at a wavelength of587.6 nm and an Abbe number between 28 and 35.

In Example 3, the optical system of any one of Examples 1-2 canoptionally be further configured such that the first incident surface,the first exiting surface, and the first glass define a refractive powerof the first lens element to be positive and between 88% and 128% of thetotal refractive power; the second incident surface, the second exitingsurface, and the second glass define a refractive power of the secondlens element to be positive and between 35% and 68% of the totalrefractive power; the third incident surface, the third exiting surface,and the third glass define a refractive power of the third lens elementto be negative and between 165% and 216% of the total refractive power;and the fourth incident surface, the fourth exiting surface, and thefourth glass define a refractive power of the fourth lens element to bepositive and between 87% and 125% of the total refractive power.

In Example 4, the optical system of any one of Examples 1-3 canoptionally be further configured such that the refractive power of thesecond lens element, divided by the refractive power of the first lenselement, is between 0.28 and 0.71; and the refractive power of thefourth lens element, divided by the refractive power of the third lenselement, is between −0.64 and −0.49.

In Example 5, the optical system of any one of Examples 1-4 canoptionally be further configured such that the first incident surface,the first exiting surface, and the first glass define a refractive powerof the first lens element to be positive and between 112% and 128% ofthe total refractive power; the second incident surface, the secondexiting surface, and the second glass define a refractive power of thesecond lens element to be positive and between 35% and 54% of the totalrefractive power; the third incident surface, the third exiting surface,and the third glass define a refractive power of the third lens elementto be negative and between 183% and 216% of the total refractive power;and the fourth incident surface, the fourth exiting surface, and thefourth glass define a refractive power of the fourth lens element to bepositive and between 91% and 125% of the total refractive power.

In Example 6, the optical system of any one of Examples 1-5 canoptionally be further configured such that the refractive power of thesecond lens element, divided by the refractive power of the first lenselement, is between 0.28 and 0.46; and the refractive power of thefourth lens element, divided by the refractive power of the third lenselement, is between −0.60 and −0.49.

In Example 7, the optical system of any one of Examples 1-6 canoptionally be further configured such that the first incident surfaceand the first exiting surface have a same radius of curvature.

In Example 8, the optical system of any one of Examples 1-7 canoptionally be further configured such that the third incident surfaceand the third exiting surface have a same radius of curvature.

In Example 9, the optical system of any one of Examples 1-8 canoptionally be further configured such that the fourth incident surfaceis planar.

In Example 10, the optical system of any one of Examples 1-9 canoptionally further include a display configured to display video anddirect light from the displayed video into the projection lens; acontroller configured to direct a video signal to the display to bedisplayed on the display; and a near-eye waveguide configured to receivelight from the projection lens and operably guide the received lighttoward a human eye.

In Example 11, the optical system of any one of Examples 1-10 canoptionally be further configured such that the projection lens furthercomprises a right-angle prism positioned along the optical axis betweenthe display and the first lens element, the right-angle prism configuredto angularly divert the optical axis by ninety degrees, the right-angleprism being formed from a crown glass having a refractive index greaterthan or equal to 1.728 at a wavelength of 587.6 nm and an Abbe numbergreater than 50.

In Example 12, the optical system of any one of Examples 1-11 canoptionally be further configured such that the projection lens furthercomprises an achromatic prism positioned along the optical axis betweenthe near-eye waveguide and the fourth lens element and configured toangularly divert the optical axis by an angle between seven degrees andnine degrees.

In Example 13, the optical system of any one of Examples 1-12 canoptionally be further configured such that the achromatic prism isformed from a first prism element, facing the fourth lens element, incontact with a second prism element, facing the near-eye waveguide; thefirst prism is formed from a flint glass having a refractive indexbetween 1.85 and 2.01 at a wavelength of 587.6 nm and an Abbe numberbetween 18.0 and 23.8; and the second prism is formed from a crown glasshaving a refractive index of 1.73 at a wavelength of 587.6 nm and anAbbe number of 54.7.

In Example 14, an optical system can include: a projection lens having apositive total refractive power and configured to direct light in alight ray bundle from a display into a near-eye waveguide, theprojection lens having an optical axis that corresponds to a center ofthe light ray bundle, the projection lens comprising: a right-angleprism positioned along the optical axis adjacent the display, theright-angle prism configured to angularly divert the optical axis byninety degrees; a first lens element positioned along the optical axis,the first lens element having a convex spherical first incident surfacefacing the right-angle prism and a convex spherical first exitingsurface facing away from the display; a second lens element positionedalong the optical axis, the second lens element having a convexspherical second incident surface facing the first lens element and aconcave spherical second exiting surface facing away from the first lenselement; a third lens element positioned along the optical axis, thethird lens element having a concave spherical third incident surfacefacing the second lens element and a concave spherical third exitingsurface facing away from the second lens element; a fourth lens elementpositioned along the optical axis, the fourth lens element having aconvex spherical or planar fourth incident surface facing the third lenselement and a convex spherical fourth exiting surface facing away fromthe third lens element toward the near-eye waveguide; and an achromaticprism positioned along the optical axis between the fourth lens elementand the near-eye waveguide, the achromatic prism configured to angularlydivert the optical axis by an angle between seven degrees and ninedegrees; wherein the first incident surface, the first exiting surface,the second incident surface, the second exiting surface, the thirdincident surface, the third exiting surface, and the fourth exitingsurface have centers that are collinear along the optical axis.

In Example 15, the optical system of Example 14 can optionally beconfigured such that the right-angle prism is formed from a crown glasshaving a refractive index greater than or equal to 1.728 at a wavelengthof 587.6 nm and an Abbe number greater than 50; the first lens elementis formed from a first glass having a refractive index between 1.72 and1.85 at a wavelength of 587.6 nm and an Abbe number between 40 and 55;the second lens element is formed from second glass having a refractiveindex between 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbenumber between 38 and 55; the third lens element is formed from a thirdglass having a refractive index greater than 1.8 at a wavelength of587.6 nm and an Abbe number between 20 and 24; and the fourth lenselement is formed from a fourth glass having a refractive index greaterthan 1.85 at a wavelength of 587.6 nm and an Abbe number between 28 and35.

In Example 16, the optical system of any one of Examples 14-15 canoptionally be configured such that the first incident surface, the firstexiting surface, and the first glass define a refractive power of thefirst lens element to be positive and between 88% and 128% of the totalrefractive power; the second incident surface, the second exitingsurface, and the second glass define a refractive power of the secondlens element to be positive and between 35% and 68% of the totalrefractive power; the third incident surface, the third exiting surface,and the third glass define a refractive power of the third lens elementto be negative and between 165% and 216% of the total refractive power;the fourth incident surface, the fourth exiting surface, and the fourthglass define a refractive power of the fourth lens element to bepositive and between 87% and 125% of the total refractive power; therefractive power of the second lens element, divided by the refractivepower of the first lens element, is between 0.28 and 0.71; and therefractive power of the fourth lens element, divided by the refractivepower of the third lens element, is between −0.64 and −0.49.

In Example 17, the optical system of any one of Examples 14-16 canoptionally be configured such that the first incident surface, the firstexiting surface, and the first glass define a refractive power of thefirst lens element to be positive and between 112% and 128% of the totalrefractive power; the second incident surface, the second exitingsurface, and the second glass define a refractive power of the secondlens element to be positive and between 35% and 54% of the totalrefractive power; the third incident surface, the third exiting surface,and the third glass define a refractive power of the third lens elementto be negative and between 183% and 216% of the total refractive power;the fourth incident surface, the fourth exiting surface, and the fourthglass define a refractive power of the fourth lens element to bepositive and between 91% and 125% of the total refractive power; therefractive power of the second lens element, divided by the refractivepower of the first lens element, is between 0.28 and 0.46; and therefractive power of the fourth lens element, divided by the refractivepower of the third lens element, is between −0.60 and −0.49.

In Example 18, the optical system of any one of Examples 14-17 canoptionally be configured such that the first incident surface and thefirst exiting surface have a same radius of curvature; the thirdincident surface and the third exiting surface have a same radius ofcurvature; and the fourth incident surface is planar.

In Example 19, an optical system can include: a display configured todisplay video; a controller configured to direct a video signal to thedisplay to be displayed on the display; a near-eye waveguide configuredto operably guide light toward a human eye; a projection lens having apositive total refractive power and configured to direct light from thedisplayed video in a light ray bundle from the display into the near-eyewaveguide, the projection lens having an optical axis that correspondsto a center of the light ray bundle, the projection lens comprising: aright-angle prism positioned along the optical axis adjacent thedisplay, the right-angle prism configured to angularly divert theoptical axis by ninety degrees, the right-angle prism being formed froma crown glass having a refractive index greater than or equal to 1.728at a wavelength of 587.6 nm and an Abbe number greater than 50; a firstlens element positioned along the optical axis and formed from a firstglass having a refractive index between 1.72 and 1.85 at a wavelength of587.6 nm and an Abbe number between 40 and 55, the first lens elementhaving a convex spherical first incident surface facing the right-angleprism and a convex spherical first exiting surface facing away from thedisplay, wherein the first incident surface, the first exiting surface,and the first glass define a refractive power of the first lens elementto be positive and between 88% and 128% of the total refractive power; asecond lens element positioned along the optical axis and formed fromsecond glass having a refractive index between 1.72 and 1.85 at awavelength of 587.6 nm and an Abbe number between 38 and 55, the secondlens element having a convex spherical second incident surface facingthe first lens element and a concave spherical second exiting surfacefacing away from the first lens element, wherein the second incidentsurface, the second exiting surface, and the second glass define arefractive power of the second lens element to be positive and between35% and 68% of the total refractive power, wherein the refractive powerof the second lens element, divided by the refractive power of the firstlens element, is between 0.28 and 0.71; a third lens element positionedalong the optical axis and formed from a third glass having a refractiveindex greater than 1.8 at a wavelength of 587.6 nm and an Abbe numberbetween 20 and 24, the third lens element having a concave sphericalthird incident surface facing the second lens element and a concavespherical third exiting surface facing away from the second lenselement, the third incident surface and the third exiting surface havinga same radius of curvature, wherein the third incident surface, thethird exiting surface, and the third glass define a refractive power ofthe third lens element to be negative and between 165% and 216% of thetotal refractive power; a fourth lens element positioned along theoptical axis and formed from a fourth glass having a refractive indexgreater than 1.85 at a wavelength of 587.6 nm and an Abbe number between28 and 35, the fourth lens element having a convex spherical or planarfourth incident surface facing the third lens element and a convexspherical fourth exiting surface facing away from the third lens elementtoward the near-eye waveguide, wherein the fourth incident surface, thefourth exiting surface, and the fourth glass define a refractive powerof the fourth lens element to be positive and between 87% and 125% ofthe total refractive power, wherein the refractive power of the fourthlens element, divided by the refractive power of the third lens element,is between −0.64 and −0.49; and an achromatic prism positioned along theoptical axis between the fourth lens element and the near-eye waveguide,the achromatic prism configured to angularly divert the optical axis byan angle between seven degrees and nine degrees; wherein the firstincident surface, the first exiting surface, the second incidentsurface, the second exiting surface, the third incident surface, thethird exiting surface, and the fourth exiting surface have centers thatare collinear along the optical axis.

In Example 20, the optical system of Example 19 can optionally beconfigured such that the first incident surface, the first exitingsurface, and the first glass define a refractive power of the first lenselement to be positive and between 112% and 128% of the total refractivepower; the second incident surface, the second exiting surface, and thesecond glass define a refractive power of the second lens element to bepositive and between 35% and 54% of the total refractive power; thethird incident surface, the third exiting surface, and the third glassdefine a refractive power of the third lens element to be negative andbetween 183% and 216% of the total refractive power; the fourth incidentsurface, the fourth exiting surface, and the fourth glass define arefractive power of the fourth lens element to be positive and between91% and 125% of the total refractive power; the refractive power of thefirst lens element, divided by the refractive power of the second lenselement, is between −0.60 and −0.49; and the refractive power of thethird lens element, divided by the refractive power of the fourth lenselement, is between 0.28 and 0.46.

What is claimed is:
 1. An optical system, comprising: a projection lenshaving a positive total refractive power and configured to direct lightin a light ray bundle from a display into a near-eye waveguide, theprojection lens having an optical axis that corresponds to a center ofthe light ray bundle, the projection lens comprising: a first lenselement positioned along the optical axis, the first lens element havinga convex spherical first incident surface facing the display and aconvex spherical first exiting surface facing away from the display; asecond lens element positioned along the optical axis, the second lenselement having a convex spherical second incident surface facing thefirst lens element and a concave spherical second exiting surface facingaway from the first lens element; a third lens element positioned alongthe optical axis, the third lens element having a concave sphericalthird incident surface facing the second lens element and a concavespherical third exiting surface facing away from the second lenselement; and a fourth lens element positioned along the optical axis,the fourth lens element having a convex spherical or planar fourthincident surface facing the third lens element and a convex sphericalfourth exiting surface facing away from the third lens element.
 2. Theoptical system of claim 1, wherein: the first lens element is formedfrom a first glass having a refractive index between 1.72 and 1.85 at awavelength of 587.6 nm and an Abbe number between 40 and 55; the secondlens element is formed from second glass having a refractive indexbetween 1.72 and 1.85 at a wavelength of 587.6 nm and an Abbe numberbetween 38 and 55; the third lens element is formed from a third glasshaving a refractive index greater than 1.8 at a wavelength of 587.6 nmand an Abbe number between 20 and 24; and the fourth lens element isformed from a fourth glass having a refractive index greater than 1.85at a wavelength of 587.6 nm and an Abbe number between 28 and
 35. 3. Theoptical system of claim 1, wherein: the first incident surface, thefirst exiting surface, and the first glass define a refractive power ofthe first lens element to be positive and between 88% and 128% of thetotal refractive power; the second incident surface, the second exitingsurface, and the second glass define a refractive power of the secondlens element to be positive and between 35% and 68% of the totalrefractive power; the third incident surface, the third exiting surface,and the third glass define a refractive power of the third lens elementto be negative and between 165% and 216% of the total refractive power;and the fourth incident surface, the fourth exiting surface, and thefourth glass define a refractive power of the fourth lens element to bepositive and between 87% and 125% of the total refractive power.
 4. Theoptical system of claim 3, wherein: the refractive power of the secondlens element, divided by the refractive power of the first lens element,is between 0.28 and 0.71; and the refractive power of the fourth lenselement, divided by the refractive power of the third lens element, isbetween −0.64 and −0.49.
 5. The optical system of claim 1, wherein: thefirst incident surface, the first exiting surface, and the first glassdefine a refractive power of the first lens element to be positive andbetween 112% and 128% of the total refractive power; the second incidentsurface, the second exiting surface, and the second glass define arefractive power of the second lens element to be positive and between35% and 54% of the total refractive power; the third incident surface,the third exiting surface, and the third glass define a refractive powerof the third lens element to be negative and between 183% and 216% ofthe total refractive power; and the fourth incident surface, the fourthexiting surface, and the fourth glass define a refractive power of thefourth lens element to be positive and between 91% and 125% of the totalrefractive power.
 6. The optical system of claim 5, wherein: therefractive power of the second lens element, divided by the refractivepower of the first lens element, is between 0.28 and 0.46; and therefractive power of the fourth lens element, divided by the refractivepower of the third lens element, is between −0.60 and −0.49.
 7. Theoptical system of claim 1, wherein the first incident surface and thefirst exiting surface have a same radius of curvature.
 8. The opticalsystem of claim 1, wherein the third incident surface and the thirdexiting surface have a same radius of curvature.
 9. The optical systemof claim 1, wherein the fourth incident surface is planar.
 10. Theoptical system of claim 1, further comprising: a display configured todisplay video and direct light from the displayed video into theprojection lens; a controller configured to direct a video signal to thedisplay to be displayed on the display; and a near-eye waveguideconfigured to receive light from the projection lens and operably guidethe received light toward a human eye.
 11. The optical system of claim10, wherein the projection lens further comprises a right-angle prismpositioned along the optical axis between the display and the first lenselement, the right-angle prism configured to angularly divert theoptical axis by ninety degrees, the right-angle prism being formed froma crown glass having a refractive index greater than or equal to 1.728at a wavelength of 587.6 nm and an Abbe number greater than
 50. 12. Theoptical system of claim 10, wherein the projection lens furthercomprises an achromatic prism positioned along the optical axis betweenthe near-eye waveguide and the fourth lens element and configured toangularly divert the optical axis by an angle between seven degrees andnine degrees.
 13. The optical system of claim 12, wherein: theachromatic prism is formed from a first prism element, facing the fourthlens element, in contact with a second prism element, facing thenear-eye waveguide; the first prism is formed from a flint glass havinga refractive index between 1.85 and 2.01 at a wavelength of 587.6 nm andan Abbe number between 18.0 and 23.8; and the second prism is formedfrom a crown glass having a refractive index of 1.73 at a wavelength of587.6 nm and an Abbe number of 54.7.
 14. An optical system, comprising:a projection lens having a positive total refractive power andconfigured to direct light in a light ray bundle from a display into anear-eye waveguide, the projection lens having an optical axis thatcorresponds to a center of the light ray bundle, the projection lenscomprising: a right-angle prism positioned along the optical axisadjacent the display, the right-angle prism configured to angularlydivert the optical axis by ninety degrees; a first lens elementpositioned along the optical axis, the first lens element having aconvex spherical first incident surface facing the right-angle prism anda convex spherical first exiting surface facing away from the display; asecond lens element positioned along the optical axis, the second lenselement having a convex spherical second incident surface facing thefirst lens element and a concave spherical second exiting surface facingaway from the first lens element; a third lens element positioned alongthe optical axis, the third lens element having a concave sphericalthird incident surface facing the second lens element and a concavespherical third exiting surface facing away from the second lenselement; a fourth lens element positioned along the optical axis, thefourth lens element having a convex spherical or planar fourth incidentsurface facing the third lens element and a convex spherical fourthexiting surface facing away from the third lens element toward thenear-eye waveguide; and an achromatic prism positioned along the opticalaxis between the fourth lens element and the near-eye waveguide, theachromatic prism configured to angularly divert the optical axis by anangle between seven degrees and nine degrees; wherein the first incidentsurface, the first exiting surface, the second incident surface, thesecond exiting surface, the third incident surface, the third exitingsurface, and the fourth exiting surface have centers that are collinearalong the optical axis.
 15. The optical system of claim 14, wherein: theright-angle prism is formed from a crown glass having a refractive indexgreater than or equal to 1.728 at a wavelength of 587.6 nm and an Abbenumber greater than 50; the first lens element is formed from a firstglass having a refractive index between 1.72 and 1.85 at a wavelength of587.6 nm and an Abbe number between 40 and 55; the second lens elementis formed from second glass having a refractive index between 1.72 and1.85 at a wavelength of 587.6 nm and an Abbe number between 38 and 55;the third lens element is formed from a third glass having a refractiveindex greater than 1.8 at a wavelength of 587.6 nm and an Abbe numberbetween 20 and 24; and the fourth lens element is formed from a fourthglass having a refractive index greater than 1.85 at a wavelength of587.6 nm and an Abbe number between 28 and
 35. 16. The optical system ofclaim 15, wherein: the first incident surface, the first exitingsurface, and the first glass define a refractive power of the first lenselement to be positive and between 88% and 128% of the total refractivepower; the second incident surface, the second exiting surface, and thesecond glass define a refractive power of the second lens element to bepositive and between 35% and 68% of the total refractive power; thethird incident surface, the third exiting surface, and the third glassdefine a refractive power of the third lens element to be negative andbetween 165% and 216% of the total refractive power; the fourth incidentsurface, the fourth exiting surface, and the fourth glass define arefractive power of the fourth lens element to be positive and between87% and 125% of the total refractive power; the refractive power of thesecond lens element, divided by the refractive power of the first lenselement, is between 0.28 and 0.71; and the refractive power of thefourth lens element, divided by the refractive power of the third lenselement, is between −0.64 and −0.49.
 17. The optical system of claim 15,wherein: the first incident surface, the first exiting surface, and thefirst glass define a refractive power of the first lens element to bepositive and between 112% and 128% of the total refractive power; thesecond incident surface, the second exiting surface, and the secondglass define a refractive power of the second lens element to bepositive and between 35% and 54% of the total refractive power; thethird incident surface, the third exiting surface, and the third glassdefine a refractive power of the third lens element to be negative andbetween 183% and 216% of the total refractive power; the fourth incidentsurface, the fourth exiting surface, and the fourth glass define arefractive power of the fourth lens element to be positive and between91% and 125% of the total refractive power; the refractive power of thesecond lens element, divided by the refractive power of the first lenselement, is between 0.28 and 0.46; and the refractive power of thefourth lens element, divided by the refractive power of the third lenselement, is between −0.60 and −0.49.
 18. The optical system of claim 17,wherein: the first incident surface and the first exiting surface have asame radius of curvature; the third incident surface and the thirdexiting surface have a same radius of curvature; and the fourth incidentsurface is planar.
 19. An optical system, comprising: a displayconfigured to display video; a controller configured to direct a videosignal to the display to be displayed on the display; a near-eyewaveguide configured to operably guide light toward a human eye; aprojection lens having a positive total refractive power and configuredto direct light from the displayed video in a light ray bundle from thedisplay into the near-eye waveguide, the projection lens having anoptical axis that corresponds to a center of the light ray bundle, theprojection lens comprising: a right-angle prism positioned along theoptical axis adjacent the display, the right-angle prism configured toangularly divert the optical axis by ninety degrees, the right-angleprism being formed from a crown glass having a refractive index greaterthan or equal to 1.728 at a wavelength of 587.6 nm and an Abbe numbergreater than 50; a first lens element positioned along the optical axisand formed from a first glass having a refractive index between 1.72 and1.85 at a wavelength of 587.6 nm and an Abbe number between 40 and 55,the first lens element having a convex spherical first incident surfacefacing the right-angle prism and a convex spherical first exitingsurface facing away from the display, wherein the first incidentsurface, the first exiting surface, and the first glass define arefractive power of the first lens element to be positive and between88% and 128% of the total refractive power; a second lens elementpositioned along the optical axis and formed from second glass having arefractive index between 1.72 and 1.85 at a wavelength of 587.6 nm andan Abbe number between 38 and 55, the second lens element having aconvex spherical second incident surface facing the first lens elementand a concave spherical second exiting surface facing away from thefirst lens element, wherein the second incident surface, the secondexiting surface, and the second glass define a refractive power of thesecond lens element to be positive and between 35% and 68% of the totalrefractive power, wherein the refractive power of the second lenselement, divided by the refractive power of the first lens element, isbetween 0.28 and 0.71; a third lens element positioned along the opticalaxis and formed from a third glass having a refractive index greaterthan 1.8 at a wavelength of 587.6 nm and an Abbe number between 20 and24, the third lens element having a concave spherical third incidentsurface facing the second lens element and a concave spherical thirdexiting surface facing away from the second lens element, the thirdincident surface and the third exiting surface having a same radius ofcurvature, wherein the third incident surface, the third exitingsurface, and the third glass define a refractive power of the third lenselement to be negative and between 165% and 216% of the total refractivepower; a fourth lens element positioned along the optical axis andformed from a fourth glass having a refractive index greater than 1.85at a wavelength of 587.6 nm and an Abbe number between 28 and 35, thefourth lens element having a convex spherical or planar fourth incidentsurface facing the third lens element and a convex spherical fourthexiting surface facing away from the third lens element toward thenear-eye waveguide, wherein the fourth incident surface, the fourthexiting surface, and the fourth glass define a refractive power of thefourth lens element to be positive and between 87% and 125% of the totalrefractive power, wherein the refractive power of the fourth lenselement, divided by the refractive power of the third lens element, isbetween −0.64 and −0.49; and an achromatic prism positioned along theoptical axis between the fourth lens element and the near-eye waveguide,the achromatic prism configured to angularly divert the optical axis byan angle between seven degrees and nine degrees; wherein the firstincident surface, the first exiting surface, the second incidentsurface, the second exiting surface, the third incident surface, thethird exiting surface, and the fourth exiting surface have centers thatare collinear along the optical axis.
 20. The optical system of claim19, wherein: the first incident surface, the first exiting surface, andthe first glass define a refractive power of the first lens element tobe positive and between 112% and 128% of the total refractive power; thesecond incident surface, the second exiting surface, and the secondglass define a refractive power of the second lens element to bepositive and between 35% and 54% of the total refractive power; thethird incident surface, the third exiting surface, and the third glassdefine a refractive power of the third lens element to be negative andbetween 183% and 216% of the total refractive power; the fourth incidentsurface, the fourth exiting surface, and the fourth glass define arefractive power of the fourth lens element to be positive and between91% and 125% of the total refractive power; the refractive power of thesecond lens element, divided by the refractive power of the first lenselement, is between 0.28 and 0.46; and the refractive power of thefourth lens element, divided by the refractive power of the third lenselement, is between −0.60 and −0.49.